Symmetry-Driven Multi-Soliton Dynamics in Bose–Einstein Condensates in Reduced Dimensions

We present a theoretical and numerical study of soliton formation and dynamics in a Bose–Einstein condensate (BEC) confined within a symmetric harmonic trap, subjected to an external barrier potential. Our investigation focuses on the role of symmetry in the system, particularly highlighting how the interplay between the harmonic confinement and the barrier shape governs the generation and evolution of multi-soliton states. Employing a reduction of the 3D Gross–Pitaevskii equation to lower-dimensional regimes, we analyze the behavior of dark solitons in 2D and 1D configurations using, for the former, exact solutions constructed from the Hirota’s bilinear formalism. We observe that the number of generated solitons exhibits a plateau-like dependence on the height of the potential barrier, reflecting the system’s symmetry and nonlinearity. Furthermore, we break the central symmetry by translating the barrier, leading to asymmetrical soliton patterns and novel dynamical behaviors. These findings underline the fundamental role of symmetry in the formation and stability of solitons in confined quantum gases, offering new perspectives on soliton engineering in trapped BECs.